﻿using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ProjectEulerSolutions
{
    /*
     * 
     * Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.

For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.

Evaluate the sum of all the amicable numbers under 10000.

     * 
     * 
     * */
    class Problem21
    {
        public static string Calculate()
        {
            int sumAmicable = 0;

            for (int i = 1; i < 10000; i++)
            {
                int sum = (int)SumDivisors(i);
                if (sum != i)
                    if ((int)SumDivisors(sum) == i)
                        sumAmicable += i;
            }


            return sumAmicable.ToString();
        }


        public static long SumDivisors(long n)
        {
            long result = 1; //1!
            for (int i = 2; i <= (n / i); i++)
            {
                if (n % i == 0)
                {
                    if (n / i == i)
                        result += i;
                    else
                        result += n / i + i;
                }
            }
            return result;
        }
    }
}
